Kevin is $3$ times as old as Daniel. $4$ years ago, Kevin was $5$ times as old as Daniel. How old is Daniel now?
Answer: We can use the given information to write down two equations that describe the ages of Kevin and Daniel. Let Kevin's current age be $k$ and Daniel's current age be $d$. The information in the first sentence can be expressed in the following equation: ${k = 3d}$ Four years ago, Kevin was $k - 4$ years old, and Daniel was $d - 4$ years old. The information in the second sentence can be expressed in the following equation: ${k - 4 = 5(d - 4)}$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $d$, it might be easiest to use our first equation for $k$ and substitute it into our second equation. Our first equation is: ${k = 3d}$. Substituting this into our second equation, we get: ${3d} {-4 = 5(d - 4)}$ which combines the information about $d$ from both of our original equations. Simplifying the right side of this equation, we get: $3 d - 4 = 5 d - 20$. Solving for $d$, we get: $2 d = 16.$ $d = 8$.